Verfügbarkeit: Fractal concepts in condensed matter physics

Fractal concepts in condensed matter physics:

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Bibliographische Detailangaben
Hauptverfasser:	Nakayama, Tsuneyoshi 1945- (VerfasserIn), Yakubo, Kousuke (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2003
Schriftenreihe:	Springer series in solid state sciences 140
Schlagworte:	Fractales Física do estado sólido Matière condensée - Mathématiques Mathematik Condensed matter > Mathematics Fractals Fraktal Statistische Mechanik Kondensierte Materie
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XIII, 206 S. graph. Darst.
ISBN:	3540050442

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MARC


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Datensatz im Suchindex

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adam_text	CONTENTS 1. INTRODUCTION ................................................ 1 2. FRACTALS ................................................... 5 2.1 FRACTAL STRUCTURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 FRACTAL DIMENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 METHODS FOR OBTAINING FRACTAL DIMENSIONS . . . . . . . . . . . . . . . . . . . . . 10 2.4 FRACTAL DIMENSION OF AEROGELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 BROWNIAN MOTION AND ITS FRACTAL NATURE . . . . . . . . . . . . . . . . . . . . . . . . 15 3. PERCOLATING NETWORKS AS RANDOM FRACTALS ...................... 19 3.1 CRITICAL EXPONENTS AND SCALING RELATIONS . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 FRACTAL DIMENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3 FINITE-SIZE SCALING AND SCALING RELATIONS . . . . . . . . . . . . . . . . . . . . . . 29 3.4 NODESLINKSBLOBS MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4. MULTIFRACTALS ............................................... 35 4.1 HIERARCHICAL RESISTOR NETWORK MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 MASS EXPONENT AND GENERALIZED DIMENSION . . . . . . . . . . . . . . . . . . . . 40 4.3 MULTIFRACTAL SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 RELATION BETWEEN * ( Q ) AND F ( * ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.5 DIRECT DETERMINATION OF F ( * ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.6 CORRELATIONS BETWEEN BOX MEASURES . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.7 PROFILES OF * ( Q ), DQ , F ( * ), AND Z ( Q ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.8 PARABOLIC APPROXIMATION AND DISTRIBUTION FUNCTIONS OF MEASURES . . . . . . . . . . . . . . . . . . . . . . . . 54 4.9 GROWTH PROBABILITY OF DLA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5. ANOMALOUS DIFFUSION ON FRACTAL NETWORKS ...................... 59 5.1 ANOMALOUS DIFFUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2 SPECTRAL DIMENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3 SPECTRAL DENSITY OF STATES OF FRACTAL NETWORKS . . . . . . . . . . . . . . . . . . 64 5.4 SCALING ARGUMENT FOR SPECTRAL DENSITY OF STATES . . . . . . . . . . . . . . . . . 65 5.5 LOCALIZATION OF EXCITATIONS ON FRACTAL NETWORKS . . . . . . . . . . . . . . . . . 66 5.6 PHONONS AND FRACTONS IN PERCOLATING NETWORKS . . . . . . . . . . . . . . . . . . 68 XII CONTENTS 6. ATOMIC VIBRATIONS OF PERCOLATING NETWORKS ..................... 71 6.1 SPECTRAL DENSITY OF STATES AND SPECTRAL DIMENSION . . . . . . . . . . . . . . . 71 6.2 MISSING MODES AT LOW FREQUENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.3 THE HUMP AT HIGH FREQUENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.4 LOCALIZED NATURE OF FRACTON EXCITATIONS. . . . . . . . . . . . . . . . . . . . . . . . 79 6.5 NETWORKS WITH VECTOR ELASTICITY: SCALING ARGUMENTS . . . . . . . . . . . . . 81 6.6 SIMULATION RESULTS FOR VECTOR ELASTICITY . . . . . . . . . . . . . . . . . . . . . . . . 86 7. SCALING ARGUMENTS FOR DYNAMIC STRUCTURE FACTORS ............... 89 7.1 DYNAMIC STRUCTURE FACTORS: INELASTIC NEUTRON SCATTERING . . . . . . . . . . 89 7.2 SINGLE-LENGTH SCALING ARGUMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.3 NUMERICAL SIMULATIONS OF S ( Q ,* ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 7.4 INELASTIC LIGHT SCATTERING IN PERCOLATING SYSTEMS . . . . . . . . . . . . . . . . 96 8. SPIN WAVES IN DILUTED HEISENBERG ANTIFERROMAGNETS .............. 101 8.1 SPIN WAVES IN PERCOLATING ANTIFERROMAGNETS . . . . . . . . . . . . . . . . . . . . 101 8.2 ANTIFERROMAGNETIC SPECTRAL DIMENSION AND THE UPPER BOUND OF * D AF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 8.3 NUMERICAL SIMULATIONS OF ANTIFERROMAGNETIC FRACTONS . . . . . . . . . . . . 107 8.4 SCALING THEORY OF S ( Q ,* ) FOR PERCOLATING ANTIFERROMAGNETS . . . . . . . 109 8.5 LARGE-SCALE SIMULATIONS FOR S ( Q ,* ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 9. ANDERSON TRANSITION ......................................... 115 9.1 COHERENT TRANSPORT OF ELECTRONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 9.2 ANDERSON LOCALIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 9.3 SCALING THEORY OF THE ANDERSON TRANSITION . . . . . . . . . . . . . . . . . . . . . 120 9.4 UNIVERSALITY CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 9.5 NUMERICAL STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9.6 DYNAMICAL PROPERTIES AT THE ANDERSON TRANSITION . . . . . . . . . . . . . . . . 134 9.6.1 SCALING FORM OF DYNAMIC QUANTITIES AT CRITICALITY . . . . . . . . . 134 9.6.2 DIFFUSION OF WAVE PACKETS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 9.6.3 TWO-PARTICLE CORRELATION FUNCTION . . . . . . . . . . . . . . . . . . . . . . 142 9.6.4 DIFFUSION LENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 10. MULTIFRACTALS IN THE ANDERSON TRANSITION ........................ 149 10.1 MULTIFRACTALITY OF A CRITICAL WAVEFUNCTION . . . . . . . . . . . . . . . . . . . . . . 149 10.2 MULTIFRACTALITY OF SPECTRAL MEASURES . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 10.3 RELATIONS BETWEEN MULTIFRACTALITY AND DYNAMICAL PROPERTIES AT THE TRANSITION POINT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 10.4 CONFORMAL INVARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 10.5 UNIVERSALITY AT HIGHER LANDAU LEVELS . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.6 FINITE-SIZE SCALING FOR THE Q TH MOMENT . . . . . . . . . . . . . . . . . . . . . . . . 172 CONTENTS XIII APPENDICES ..................................................... 177 A. MULTIFRACTALITY OF THE HRN MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 B. SPECTRAL DIMENSIONS FOR DETERMINISTIC FRACTALS . . . . . . . . . . . . . . . . . . 182 B.1 SIERPINSKI GASKET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 B.2 MANDELBROT*GIVEN FRACTAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 C. DIFFUSION AND DYNAMICS ON NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . . 186 C.1 ATOMIC VIBRATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 C.2 SPIN WAVES IN DILUTED FERRO- AND ANTIFERROMAGNETS . . . . . . . 191 C.3 SUPERCONDUCTING NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 D. WIGNER DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 REFERENCES ..................................................... 197 SUBJECT INDEX ................................................... 203
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spelling	Nakayama, Tsuneyoshi 1945- Verfasser (DE-588)124884199 aut Fractal concepts in condensed matter physics T. Nakayama, K. Yakubo Berlin [u.a.] Springer 2003 XIII, 206 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid state sciences 140 Includes bibliographical references and index Fractales Física do estado sólido larpcal Matière condensée - Mathématiques Mathematik Condensed matter Mathematics Fractals Fraktal (DE-588)4123220-3 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Fraktal (DE-588)4123220-3 s DE-604 Statistische Mechanik (DE-588)4056999-8 s Yakubo, Kousuke Verfasser aut Erscheint auch als Online-Ausgabe 978-3-662-05193-1 Springer series in solid state sciences 140 (DE-604)BV000016582 140 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010317155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Nakayama, Tsuneyoshi 1945- Yakubo, Kousuke Fractal concepts in condensed matter physics Springer series in solid state sciences Fractales Física do estado sólido larpcal Matière condensée - Mathématiques Mathematik Condensed matter Mathematics Fractals Fraktal (DE-588)4123220-3 gnd Statistische Mechanik (DE-588)4056999-8 gnd Kondensierte Materie (DE-588)4132810-3 gnd
subject_GND	(DE-588)4123220-3 (DE-588)4056999-8 (DE-588)4132810-3
title	Fractal concepts in condensed matter physics
title_auth	Fractal concepts in condensed matter physics
title_exact_search	Fractal concepts in condensed matter physics
title_full	Fractal concepts in condensed matter physics T. Nakayama, K. Yakubo
title_fullStr	Fractal concepts in condensed matter physics T. Nakayama, K. Yakubo
title_full_unstemmed	Fractal concepts in condensed matter physics T. Nakayama, K. Yakubo
title_short	Fractal concepts in condensed matter physics
title_sort	fractal concepts in condensed matter physics
topic	Fractales Física do estado sólido larpcal Matière condensée - Mathématiques Mathematik Condensed matter Mathematics Fractals Fraktal (DE-588)4123220-3 gnd Statistische Mechanik (DE-588)4056999-8 gnd Kondensierte Materie (DE-588)4132810-3 gnd
topic_facet	Fractales Física do estado sólido Matière condensée - Mathématiques Mathematik Condensed matter Mathematics Fractals Fraktal Statistische Mechanik Kondensierte Materie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010317155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000016582
work_keys_str_mv	AT nakayamatsuneyoshi fractalconceptsincondensedmatterphysics AT yakubokousuke fractalconceptsincondensedmatterphysics

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